(Photo)electrochemicalMethodsfortheDeterminationof...

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Hindawi Publishing Corporation Advances in Physical Chemistry Volume 2011, Article ID 786759, 20 pages doi:10.1155/2011/786759 Review Article (Photo)electrochemical Methods for the Determination of the Band Edge Positions of TiO 2 -Based Nanomaterials Radim Beranek 1, 2, 3 1 Faculty of Chemistry and Biochemistry, Ruhr University Bochum, Universit¨ atstr 150, NC4/073, D-44780 Bochum, Germany 2 Materials Research Department, Ruhr University Bochum, D-44801 Bochum, Germany 3 Research Department Interfacial Systems Chemistry, Ruhr University Bochum, D-44801 Bochum, Germany Correspondence should be addressed to Radim Beranek, [email protected] Received 30 September 2011; Accepted 15 December 2011 Academic Editor: Konstantin Neyman Copyright © 2011 Radim Beranek. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. TiO 2 -based nanomaterials play currently a major role in the development of novel photochemical systems and devices. One of the key parameters determining the photoactivity of TiO 2 -based materials is the position of the band edges. Although its knowledge is an important prerequisite for understanding and optimizing the performance of photochemical systems, it has been often rather neglected in recent research, particularly in the field of heterogeneous photocatalysis. This paper provides a concise account of main methods for the determination of the position of the band edges, particularly those suitable for measurements on nanostructured materials. In the first part, a survey of key photophysical and photochemical concepts necessary for understanding the energetics at the semiconductor/solution interface is provided. This is followed by a detailed discussion of several electrochemical, photoelectrochemical, and spectroelectrochemical methods that can be applied for the determination of band edge positions in compact and nanocrystalline thin films, as well as in nanocrystalline powders. 1. Introduction Although first scientific reports of photoinduced eects of titanium dioxide on chemical reactions were available already more than ninety years ago [18], it was first in the 1970s that potential practical applications of TiO 2 pho- toelectrochemistry and photocatalysis have been fully rec- ognized. This was particularly due to the pioneering work of Fujishima and Honda on solar-driven water splitting into hydrogen and oxygen using a TiO 2 photoanode [911], which promised utilization of TiO 2 -based materials for solar energy conversion and storage [1216]. In following years further photochemical applications of TiO 2 have been realized, most of them motivated particularly by the advanta- geous combination of its low cost, nontoxicity, and excellent stability against photocorrosion. One important example is the rapidly growing field of heterogeneous photocatalysis [1725], in which TiO 2 has been successfully employed in photooxidation reactions utilizing aerobic oxygen for the complete removal of pollutants from water and air [1722, 2439], in preparation of superhydrophilic and antifogging surfaces [4043], in photocatalytic organic syntheses [4449], or in antitumor medicinal applications [5054]. Importantly, although the bandgap energy of TiO 2 is rather large (for anatase 3.2 eV; 390 nm) and direct band- to-band excitation can therefore only be achieved by high- energy UV light, the utilization of TiO 2 is not confined to UV-light-driven applications. Drawing on the fundamental studies on dye sensitization of other wide bandgap semicon- ductors (ZnO, SnO 2 ) in the 1960s [5559], attaching visible- light-absorbing organic dyes to the surface of TiO 2 [60, 61] has led to fabrication of regenerative dye-sensitized solar cells with the overall solar conversion eciencies exceeding 10% [6264]. Other sensitization approaches utilize chro- mophores like semiconductor quantum dots [6570], plas- monic metal nanocrystals [7175], simple coordination compounds like chloroplatinate (IV) complexes [29, 32, 76] or ferrocyanide ions [7779], stable polymeric com- pounds [38, 39, 8083], or metal ions (Cu 2+ , Fe 3+ ) grafted onto the TiO 2 surface [84, 85]. In contrast to these surface- confined sensitization protocols, bulk-doping of TiO 2 has also attracted significant interest. In the latter approach,

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Hindawi Publishing CorporationAdvances in Physical ChemistryVolume 2011, Article ID 786759, 20 pagesdoi:10.1155/2011/786759

Review Article

(Photo)electrochemical Methods for the Determination ofthe Band Edge Positions of TiO2-Based Nanomaterials

Radim Beranek1, 2, 3

1 Faculty of Chemistry and Biochemistry, Ruhr University Bochum, Universitatstr 150, NC4/073, D-44780 Bochum, Germany2 Materials Research Department, Ruhr University Bochum, D-44801 Bochum, Germany3 Research Department Interfacial Systems Chemistry, Ruhr University Bochum, D-44801 Bochum, Germany

Correspondence should be addressed to Radim Beranek, [email protected]

Received 30 September 2011; Accepted 15 December 2011

Academic Editor: Konstantin Neyman

Copyright © 2011 Radim Beranek. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

TiO2-based nanomaterials play currently a major role in the development of novel photochemical systems and devices. Oneof the key parameters determining the photoactivity of TiO2-based materials is the position of the band edges. Although itsknowledge is an important prerequisite for understanding and optimizing the performance of photochemical systems, it hasbeen often rather neglected in recent research, particularly in the field of heterogeneous photocatalysis. This paper providesa concise account of main methods for the determination of the position of the band edges, particularly those suitable formeasurements on nanostructured materials. In the first part, a survey of key photophysical and photochemical concepts necessaryfor understanding the energetics at the semiconductor/solution interface is provided. This is followed by a detailed discussion ofseveral electrochemical, photoelectrochemical, and spectroelectrochemical methods that can be applied for the determination ofband edge positions in compact and nanocrystalline thin films, as well as in nanocrystalline powders.

1. Introduction

Although first scientific reports of photoinduced effectsof titanium dioxide on chemical reactions were availablealready more than ninety years ago [1–8], it was first inthe 1970s that potential practical applications of TiO2 pho-toelectrochemistry and photocatalysis have been fully rec-ognized. This was particularly due to the pioneering workof Fujishima and Honda on solar-driven water splittinginto hydrogen and oxygen using a TiO2 photoanode [9–11], which promised utilization of TiO2-based materials forsolar energy conversion and storage [12–16]. In followingyears further photochemical applications of TiO2 have beenrealized, most of them motivated particularly by the advanta-geous combination of its low cost, nontoxicity, and excellentstability against photocorrosion. One important example isthe rapidly growing field of heterogeneous photocatalysis[17–25], in which TiO2 has been successfully employed inphotooxidation reactions utilizing aerobic oxygen for thecomplete removal of pollutants from water and air [17–22,24–39], in preparation of superhydrophilic and antifogging

surfaces [40–43], in photocatalytic organic syntheses [44–49], or in antitumor medicinal applications [50–54].

Importantly, although the bandgap energy of TiO2 israther large (for anatase 3.2 eV; ∼ 390 nm) and direct band-to-band excitation can therefore only be achieved by high-energy UV light, the utilization of TiO2 is not confined toUV-light-driven applications. Drawing on the fundamentalstudies on dye sensitization of other wide bandgap semicon-ductors (ZnO, SnO2) in the 1960s [55–59], attaching visible-light-absorbing organic dyes to the surface of TiO2 [60, 61]has led to fabrication of regenerative dye-sensitized solarcells with the overall solar conversion efficiencies exceeding10% [62–64]. Other sensitization approaches utilize chro-mophores like semiconductor quantum dots [65–70], plas-monic metal nanocrystals [71–75], simple coordinationcompounds like chloroplatinate (IV) complexes [29, 32,76] or ferrocyanide ions [77–79], stable polymeric com-pounds [38, 39, 80–83], or metal ions (Cu2+, Fe3+) graftedonto the TiO2 surface [84, 85]. In contrast to these surface-confined sensitization protocols, bulk-doping of TiO2 hasalso attracted significant interest. In the latter approach,

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transition metals [86–88] or main-group elements like car-bon [35, 89], nitrogen [31, 90–97], and sulfur [98, 99] areintroduced into the lattice of titania resulting in formationof intrabandgap donor and acceptor levels, allowing thus forvisible light (λ > 400 nm) excitation. Apart from the fieldsof solar cells and photocatalysis, the visible light-responsiveTiO2 materials opened up a route for further developmentsincluding photoelectrochemistry-based sensors [100, 101]and light-addressable photoelectrochemical optoelectronicdevices [102–106].

Obviously, many applications can benefit from TiO2

materials with fine-tuned structural and surface characteris-tics. Particularly nanostructured and mesoporous materialswith a large surface-to-volume ration are highly prof-itable for most applications. This motivated the develop-ment of a great variety of synthetic protocols which allowfor fabrication of TiO2 with well-defined morphologies onthe micro- and nanoscale. These include, for example, na-noporous spheres [107], nanotubes [108, 109], hierarchi-cal nanodendrite-nanoparticle composites [110], organizedmesoporous TiO2 films with controlled crystallinity [111,112], nanoparticles with distinct crystal facets [113, 114],or TiO2 inverse opals materials exhibiting photonic bandgap[115–117]. In addition, the modification of surface catalyticproperties has been achieved, for instance, by coupling TiO2

with gold nanostructures [118], graphene [119], or reducedgraphene oxide [120, 121].

Notwithstanding the huge variety of different TiO2-basedmaterials, it is important to realize that the fundamentalbasis for all photochemical applications of TiO2 is itssemiconducting electronic structure [122, 125–129]. In otherwords, it is the energy band structure that underlies the pho-toactivity of TiO2-based materials, whereby the position ofthe band edges on the electrochemical potential scale exertsa crucial influence on the operation of the photochemicalsystem. This can be well exemplified in Figure 1. A typicalphotocatalytic reaction at small TiO2 particles is initiated byabsorption of a UV light photon, whereby a pair of charges isgenerated—an electron in the conduction band and a hole inthe valence band (Figure 1(a)). The photogenerated chargescan either recombine or undergo an interfacial electrontransfer process, whereby the electron reduces an electronacceptor species A to a primary reduction product A−•, andthe hole oxidizes an electron donor species to D+•. Hence, forexample, during a typical photocatalytic oxidation of organicpollutants on TiO2 in aqueous solutions, the reacting holesare scavenged either directly by the pollutant or by adsorbedhydroxyl ions to produced hydroxyl radicals which can thenoxidize the pollutant due to their high oxidizing power.Simultaneously, the photogenerated electrons reduce molec-ular oxygen to a superoxide radical (EO2/O2

−• = −0.16 Vversus NHE [130]) which can then undergo further reactionsto produce hydroxyl radicals [17, 131–134]. It is obviousthat the positions of the conduction and valence band edgesare of crucial importance here since these give informationon the reductive and oxidative power of photogeneratedelectrons and holes, respectively. Interestingly, the productof the one-hole oxidation of some electron donors—like, forexample, the methoxy radical as a primary oxidation product

of methanol (Figure 1(b))—is a very strong reducing agentthat can inject an electron into the conduction band ofTiO2 and is thereby further oxidized to formaldehyde.Since this generation of two electrons in the conduc-tion band upon absorption of one photon has been firstobserved during photocurrent measurements, it has beencoined as the photocurrent-doubling effect (photocurrent-multiplication effect) [125]. It goes without saying that theposition of the conduction band edge on the potential scalewill again play an essential role for the efficiency of theelectron injection in such a case. Obviously, similar consid-eration will be also valid in cases when the photoprocessis based on light absorption by a sensitizer, typically a dye(Figure 1(c)). Here, the dye gets into an excited state fromwhich it injects an electron into the conduction band of asemiconductor and is thereby oxidized. Alternatively to thisphotoinduced electron transfer scenario, in case of a strongcoupling between the sensitizer and TiO2 the so-called directoptical electron transfer from the chromophore’s HOMO intothe conduction band of TiO2 can occur, as known, for exam-ple, for TiO2 covalently sensitized with catechol [135–137],chlorophenols [138, 139], or polymeric compounds [140].In case of TiO2-assisted photooxidation reactions based onsensitization, one often speaks about “indirect photocataly-sis” since the reaction is not initiated through direct photonabsorption by TiO2 (“direct photocatalysis”; Figure 1(a)),but instead indirectly, through the light absorption by a dye[24, 25, 34, 37]. At any rate, the position of the conductionband edge must be positive enough in order to allow for theinjection from the dye, and at the same time negative enough,in order to allow for further electron transfer to suitableacceptors in the solution (e.g., oxygen).

From the above stated, it is clear that the positions of theband edges exert a crucial influence on the photoactivity ofTiO2-based materials. In this context, it is rather surprisingthat the determination of the band edge position is still onlyvery rarely directly addressed experimentally, particularly inresearch directed to the development of new photocatalysts.This causes a serious lacuna in our understanding of thephotoactivity of such novel materials since the position ofthe band edges in many cases cannot be simply predicted ortaken from the literature data. This is due to the fact that theband edge positions of TiO2-based materials will normallydepend on surface charging. This will be highly dependentnot only on the ionic conditions in a concrete electrolyte(pH, specific adsorption of ions), but also on the surfacestructure and composition of the material, which, in turn,will depend on the particular synthetic strategy used for thefabrication. The aim of this paper is to review various meth-ods for the measurement of the band edge positions of TiO2-based materials. The focus will be particularly on nanostruc-tured materials used in photocatalysis and other applicationsoperating in aqueous electrolytes. The paper will start witha short summary of some fundamental concepts of semi-conductor photophysics and photochemistry (quasi-Fermilevels, flatband potential, pH dependence of band edges)that are directly relevant for understanding the problem ofband edge determination. Then, a theoretical approach tothe calculation of the band edges position, together with

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Potential(V versus NHE)

CB

VB

A

D

3

2

1

0

−1

A−•

D+•

hAUV

(a)

CB

VB

e−•CH2OH+ +

CH3OHhA

UV

H2CO + H+

(b)

CB

VB

hAVIS

S0

S∗e−

S+

(c)

Potential(V versus NHE)

Energy(eV versus vacuum level)

Increasingelectronenergy

Increasingelectrodepotential

−1

−2

−3

−4

−5

−6

−7

−1

−2

−3

−4

2

1

0

0

(d)

Figure 1: Schematic view of different TiO2-assisted photoprocesses. (a) Direct photocatalysis initiated by excitation of an electron from thevalence band (VB) to the conduction band (CB) of TiO2. (b) Mechanism of “photocurrent multiplication” at an irradiated TiO2 electrodein the presence of methanol. (c) Sensitization of TiO2 by a dye: the dye is photoexcited with visible light from its ground state S0 to excitedstate S∗, injects an electron to the conduction band of TiO2, and is thereby oxidized to S+. All recombination pathways are omitted forthe sake of clarity. Whereas the common convention in solid state physics relates the positions of band edges with respect to the vacuumlevel, in photoelectrochemistry and photocatalysis, the potentials are usually given with respect to the normal hydrogen electrode (NHE;ENHE = 0 V). On the energy scale, the NHE is reported to lie at −4.44 ± 0.02 eV (at 298.15 K) with respect to the vacuum level [122]; formore details, see [123, 124].

the application of conventional spectroscopic and contactpotential difference measurements, will be shortly discussed.This will be followed by a detailed discussion of variouselectrochemical, photoelectrochemical, and spectroelectro-chemical methods that can be applied to measurements onTiO2-based materials in the form of thin compact films,porous nanocrystalline layers, and nanocrystalline powders.

2. Theory and Fundamental Concepts

2.1. Quasi-Fermi Levels and Flatband Potential. TiO2 is typi-cally found in one of its three main crystal structures: rutile(tetragonal), anatase (tetragonal), or brookite (orthorhom-bic). Out of these, anatase is the polymorph most widelyused for photocatalytic and photoelectrochemical purposes.It is noteworthy that the conduction band edge states havepredominantly the Ti 3d character, while the valence-bandedge states have the O 2p character. Importantly, due toits inherent nonstoichiometry (oxygen vacancies), TiO2 istypically a rather heavily doped n-type semiconductor. This

means that its Fermi level (EF) is typically right below theconduction band edge (EC). From the thermodynamic pointof view, the Fermi level is the electrochemical potential of theelectron in the solid. Equivalently, from the statistical pointof view, the Fermi level is the energy at which the probabilityof an energy level being occupied by an electron (the Fermifunction) is 0.5 (Note, however, that this does not implythat the level at the Fermi energy is populated by electronsbecause the population depends upon the product of theFermi function and the electron density of states). Hence,the Fermi level describes the occupation of energy levels ina semiconductor at thermodynamic equilibrium. However,the condition of thermodynamic equilibrium is not alwaysfulfilled—particularly when excess electrons and holes arephotogenerated under illumination or injected under electricbias. Accordingly, the electron and hole densities in theconduction and valence band are not described by the sameFermi level but by a quasi-Fermi level of electrons ( ∗EFn) anda quasi-Fermi level of holes ( ∗EFp), respectively (Figure 2)[125, 126, 128]. In general, the density of majority carriers

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CB

VB

x

EV

EF

E

E

C

(a)

CB

VB

x

∗EFn

∗EFp

EV

E

E

C

hA

(b)

CB

VB

x

∗EFn

∗EFp

EV

E

hA

EC

(c)

Figure 2: Fermi levels and quasi-Fermi levels of electrons and holes for an n-type semiconductor: (a) at thermodynamic equilibrium (in thedark); (b) and (c) under illumination; (c) local excitation; x is the distance from the semiconductor surface (adapted from [128]).

(electrons in case of TiO2) does not significantly increaseupon illumination and the quasi-Fermi level for majoritycarriers is normally almost the same as the Fermi level atequilibrium. In contrast, the density of minority carriers(holes) can be increased by many orders of magnitude, whichthen leads to a shift of the quasi-Fermi level of holes ( ∗EFp)downwards to the vicinity of the valence band edge.

It should be also noted that the generation of electron-hole pairs often occurs locally near the semiconductorsurface due to the small penetration depth of light, whichleads to variations in the quasi-Fermi level of holes with thedistance from the surface (Figure 2(c)). Importantly, in caseof heavily doped n-type metal oxides like TiO2, the lowerconduction band edge, EC, practically merges with the quasi-Fermi level for electrons, ∗EFn, (|EC− ∗EFn | < 0.1V) [125].Therefore, as will be discussed below in more detail, thedetermination of the conduction band edge often translatesinto the measurement of the position of the quasi-Fermi levelof electrons. Once this is known, the position of the valenceband edge can be simply calculated by adding the valueof bandgap energy, that is, typically determined by optical[128, 141–151] or photoelectrochemical methods [152–156].

Another important concept, particularly in case of com-pact flat TiO2 films that behave similarly to single crystalsemiconductors, is the flatband potential. First, let us con-sider the energetic situation at the n-type semiconductor/electrolyte interface before and after the contact of the twophases (Figure 3). After the contact of the semiconductorsurface with the electrolyte, the thermodynamic equilibriumon both sides of the interface must be established [125–128,157]. In other words, the Fermi level of the semiconductorEF is adjusted to the Fermi level of the electrolyte EF,redox. Thelatter can be considered nearly constant because the numberof available states per unit energy in the solution typically farexceeds the number present in a semiconductor. This equi-libration happens through electron transfer across the inter-face, which results in formation of the space-charge layer—also called the “depletion layer” since the surface region ofthe semiconductor is depleted of its majority carriers. It isimportant to realize that, in the case of an n-type semicon-ductor, this interfacial charge-transfer process produces an

excess of positive charges in the semiconductor (immobilecharges of ionized donors) and an excess of negative chargesin the electrolyte. With more electrons exchanged, the elec-tric field of the negative charges on the solution side hindersfurther electron transfer so that the equilibrium is establishedin which no net charge flow occurs. As a consequence, thebands are bent upwards, which can be understood in termsof a continuously growing barrier for interfacial electrontransfer when moving from the bulk of the semiconductor tothe interface due to the continuously less efficient screeningof the negative charges in the solution by the positive chargesin the depletion layer [127]. The height of the barrier is theenergy difference between the conduction band edge in thebulk (EC) semiconductor and the conduction band edge atthe surface (EC,S) and corresponds to the potential drop inthe space-charge layer US.

The charge distribution scenario at semiconductor/elec-trolyte interface is summarized in Figure 4. Importantly,three distinct double layers can be distinguished at theinterface. First, it is the semiconductor space-charge layerwith positive charges in the form of ionized donors and thecounter negative charge located at the surface. The secondone is the Helmholtz double layer consisting of the innerHelmholtz plane (IHP) and the outer Helmholtz plane(OHP). The first is located at the semiconductor surface,and the charge is in the surface states or at the location ofspecifically adsorbed ions, whereas the latter denotes theposition of the closest approach of hydrated mobile ions.Finally, there is the Gouy-Chapman layer which is extendedregion with an excess of free ions of one sign. Essentially,the double layers act as parallel-plate capacitors connectedin series with capacitances CSC, CH, and CG representingthe capacitance of the space-charge layer, the capacitanceof the Helmholtz double layer, and the capacitance of theGouy-Chapman layer, respectively, whereby CG can betypically neglected for electrolytes containing relatively highconcentrations of redox species (Figure 4(d)).

The simplest quantitative description of the situationat the semiconductor/electrolyte interface [125–129, 157] isanalogous to the Schottky diode model and is based on thefollowing assumptions: (i) ideal, crystalline semiconductor,

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Density of states

(a)

Distance Density of statesDistance

(b)

Local vacuum level Local vacuum level

ECEF

ECEF

CB

CB

IES

IES

IEE

EV

EV

VB

VB

χS

χS

χE IEEχ

E

Dred (occupied)Dred (occupied)

Dox (empty)

Dox (empty)

λλ

λ λ

E E

W

US

ΦS

ΦS

ΦE

E0F,redox

E0F,redox

ΦE

Figure 3: Schematic energy model of the n-type semiconductor/electrolyte interface before (a) and after (b) the establishment ofequilibrium. The presence of surface states in the semiconductor is neglected. Dred and Dox correspond to the distribution functions ofthe density of states for reduced and oxidized species, respectively, of the redox system (the energy distribution of reduced and oxidizedspecies is different due to different solvation; λ is the reorganization energy). Φ, χ, and IE are the work function, electron affinity, andionization energy, respectively, of the semiconductor (index S) and of the electrolyte (index E).

homogeneous donor level near the conduction band (oxygenvacancies in the form of Ti3+ sites in case of TiO2) withall donors ionized (all the electrons from the Ti3+ donorshave been thermally excited to the conduction band); (ii) nosurface states; (iii) potential drop in the Helmholtz layer canbe neglected. The potential and charge distribution withinthe space-charge layer can be then described by a one-dimensional Poisson equation:

∂2ϕ

∂x2 = −1εε0

ρ, (1)

where ϕ is potential, x is distance, ε and ε0 are the relativepermittivity of the semiconductor and the permittivity ofvacuum, respectively, and ρ is the volume charge density.After two integrations assuming ρ = qN (q is the elementarycharge; N is the doping concentration) and the boundaryconditions dϕ/dx = 0 for x = W and ϕ = 0 for x = W

(see [125, 126, 128] for details), one obtains the followingrelation for the width of the space-charge layer W :

W =∣∣∣∣∣

2εε0

qN

(

US − kT

q

)∣∣∣∣∣

1/2

, (2)

where US is the potential drop in the space-charge layerwhich can be obtained as

US = Eappl − EFB (with external polarization) (3)

or

US = EF,redox − EFB (without external polarization),(4)

where Eappl is externally applied potential and EFB is thepotential at which US = 0 and the bands in the semicon-ductor are “flat” (flatband potential). It is now clear that thevalue of EFB is of fundamental significance since it gives adirect information on the position of the conduction band

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UH UG

CSC CH

IHP OHP

Semiconductor Helmholtz

layer

Gouy-Chapman

region

Normal concentration

region

Semiconductor

Distance

Charge

Distance

Potential

W

(a)

(b)

(c)

(d)

bulk space-charge layer

US

Figure 4: Schematic view of the electric double layers at the n-type semiconductor/aqueous electrolyte interface (a) with correspondingcharge (b) and potential (b) distributions. US is the potential drop across the space-charge layer, UH is the potential drop in the Helmholtzlayer, and UG represents the drop in the Gouy-Chapman layer; (d) the equivalent circuit for the interface assuming that UG can be neglected.

edge at the n-type semiconductor’s surface (EC,S), assumingthat the difference between EFB and EC,S is very small fordoped semiconductors. In other words, the determination ofthe conduction band edge of thin compact TiO2 films oftentranslates into the measurement of the flatband potential (formore details, see below). However, it should be emphasizedthat, in the context of nanomaterials, the above describedformalism applies only to thin compact highly doped TiO2

films that behave in a manner similar to compact crystallinesemiconductors. In contrast, in small TiO2 particles andin highly porous nanocrystalline electrodes, the formationof the space-charge layer is improbable due to the very

small crystallite size [158–163]. In other words, the nearlydepleted small TiO2 crystals do not contain enough electronsin order to create an effective space-charge layer. Severalmethods suitable for the determination of band edges in suchnanocrystalline systems will be presented below.

2.2. pH Dependence of the Position of Band Edges. The posi-tion of the band edges at the surface (EC,S) is determined bythe charge at the surface, that is, by the potential drop in theHelmholtz layer UH:

EC,S = E0C,S − qUH, (5)

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Ti

OO

Ti

O

H

Ti

OO OO

Ti

OH

OH

Ti

Ti

H

H

H

HO

(+)

(+)

(+)

pH < pHIEP pH > pHIEPpH = pHIEP

+ H+

O(−)

O(−)

+ OH−

Figure 5: Simplified scheme of the protonation and deprotonationof hydroxylated TiO2 surface leading to positive and negative netcharge at the surface, respectively. The isoelectric point (pHIEP) ofTiO2 is typically ca. 5.8–7.5 [125, 164–167]. The pKA values ofmonodentate and bidentate OH groups are reported to be 12.7 and2.9, respectively [166].

where E0C,S is the position (on the energy scale) of the

conduction band edge at the surface at UH = 0. TheHelmholtz double layer at semiconductors is typically deter-mined through adsorption and desorption processes, whichis particularly true for ionic oxide semiconductors like TiO2

in aqueous electrolytes. In this case, the protons and hydroxylgroups play an essential role while the specific adsorption ofother ions can be in most cases neglected.

In essence, the lattice Ti atoms act as Lewis acid sitesand make the adsorption of hydroxyl ions possible, whereasthe bridging lattice oxygen attracts protons and acts therebyas a Lewis base site. Hence, depending on the pH, thesemiconductor surface becomes charged either positively ornegatively (Figure 5). The pH value at which the net surfacecharge is zero is called the isoelectric point (pHIEP) or thepoint of zero zeta potential (pzzp). (Here, it should be notedthat pHIEP and pzzp are not necessarily identical with thepoint of zero charge, pzc, that denotes the pH value atwhich H+ and OH− are adsorbed in equal amounts; whenother ions than H+ and OH− are present and influence thecharging of the surface, the pzc and the pHIEP are not equal).The pH dependence of the conduction band edge at thesurface can be then derived as follows [125]. Assuming pH <pHIEP, we obtain the following equilibrium reaction:

H3O+ � HS+ + H2O, (6)

where H3O+ is a hydroxonium ion in the solution and HS+ is

an adsorbed proton. The equilibrium is described by[

HS+]

[

H3O+] = exp(

−ΔG

kT

)

= A exp(−qUH

kT

)

, (7)

where ΔG is the free Gibbs energy, UH is the potential dropin the Helmholtz double layer, and A is a constant (assumingthat ΔG varies linearly with UH). Assuming [H3O+] �[HS

+], the following relation can be obtained:

qUH = B + kT ln[

H3O+] = B − 2.3kT pH, (8)

in which B = 2.3kT (pHIEP) assuming UH = 0 at pHIEP. Bycombining (5) and (8), we obtain now

EC,S = E0C,S + 2.3kT

(

pH− pHIEP

)

. (9)

Accordingly, with increasing pH, the band edges at thesurface shift to higher energies (on the energy scale), that is,to more cathodic potentials (on the electrode potential scale),whereby the shift at 298 K is typically ∼ 0.059 V/pH unit.

2.3. Non-Ideal Behavior due to Surface States. The theoreticalconsiderations described in Sections 2.1 and 2.2 assume thatthe charging of the semiconductor surface (i.e., the positionof its band edges) is independent of the applied potential(applied bias voltage is effectively “consumed” within thespace-charge layer) or irradiation (minority charge carriersare efficiently scavenged by species in the electrolyte). How-ever, many semiconductors can have localized surface energylevels in the bandgap—the so-called “surface states”—whichare typically related to crystal defects or surface damage,or they may result from surface reactions occurring inthe dark or under illumination [128, 168, 169]. Obviously,relatively high density of surface states can be present at thesurface of doped or surface-modified TiO2-based materials.It is important to realize that the presence of surface statescan have significant effects on the position of band edges.During electrode polarization, the Fermi level can match theenergy level of the surface states, which will lead to theircharging. This might result in the change of the net chargeat the surface (i.e., change in the potential drop across theHelmholtz layer), which will cause a shift of the band edgepositions. Similarly, during irradiation, the surface statesmay act as traps for photogenerated charge carriers. Thus,for example, the minority charge carriers (holes in case of n-type TiO2) or charged surface intermediates can accumulateat the surface, which will again lead to changes in the surfacecharging and result in “unpinning” of band edges [170].In photoelectrochemical experiments, these problems canbe to some extent avoided by adding efficient scavengers ofminority charge carriers into the electrolyte [171].

2.4. Theoretical Predictions of the Position of Band Edges.Butler and Ginley introduced a theoretical approach for theprediction of the position of band edges using the followingrelation [125, 164]:

E0C,S = Ee − X +

12Eg, (10)

where Ee is the energy of free electrons on the hydrogenscale (4.44 ± 0.02 eV), Eg is the bandgap energy, and Xis the Sanderson electronegativity of the semiconductor,expressed as the geometric mean of the electronegativitiesof the constituent atoms, which are defined after Mullikenas the arithmetic mean of the atomic electron affinity andthe first ionization energy (both in eV). Calculation for TiO2

gives X = 5.8 eV, which (assuming (1/2)Eg = 1.6 eVfor anatase) yields the value of E0

C,S of +0.24 eV (relative tostandard hydrogen electrode on the energy scale, i.e.,−0.24 Vversus NHE on the electrode potential scale). Interestingly,this result is only by∼0.1 V more negative than experimentalresults obtained by measurements on anatase single crystals[172]. Although several more sophfisticated theories basedon DFT calculations have been developed recently [173–175], the theoretical predictions cannot be always expected

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8 Advances in Physical Chemistry

to yield sufficiently reliable results, mainly in case of dopedand surface-modified TiO2-based materials.

2.5. Spectroscopic and Contact Potential Difference Techniques.Obviously, some key quantities related to the positions ofenergy bands (see Figure 3) can be obtained also fromspectroscopic and contact potential difference measurementsperformed in a “dry” (or “semidry”) state. Thus, for example,the ionization energy of the semiconductor (IES, defined asthe energy needed to excite an electron from the valenceband edge at the surface to the local vacuum level) can bemeasured by photoemission spectroscopy (e.g., UPS) [176].On the other hand, the Kelvin probe method can be used fordetermination of the contact potential difference (CPD), thatis, of the difference between the work function of a semicon-ductor and the work function of the metal tip of the probe(with known position on the energy vacuum scale) [177].Moreover, the latter technique can be combined with illu-mination in the so-called surface photovoltage spectroscopyin which the changes of the CPD (i.e., of surface voltage)upon illumination are measured [178, 179]. Importantly, thesaturation surface photovoltage is then directly related tothe difference of the position of the Fermi level in the darkand the position of the quasi-Fermi level under illumination[180]. As an alternative to the Kelvin probe technique, thesurface photovoltage can be also measured directly utilizing ametal-insulator-semiconductor structure and using choppedillumination in conjunction with lock-in detection of thesurface photovoltage signal [178, 179]. Importantly in thecontext of this paper, a standard surface photovoltagemeasurement can typically be performed also in the presenceof adsorbents like water molecules at the surface of thesemiconductor (“semidry” state) [181]. Moreover, the Kelvinprobe measurements of photoelectrodes immersed intoelectrolyte have been reported, whereby the electrode and theelectrolyte were separated from the Kelvin probe tip by a verythin glass plate [182]. This method has been, for example,used for the estimation of the quasi-Fermi level in the TiO2

nanocrystalline layers of dye-sensitized solar cells [183].A more detailed discussion of these approaches is

beyond the scope of this paper. Herein, we deal mainly withTiO2-based materials for use in photocatalysis and pho-toelectrochemistry and the focus is on electrochemicaland photoelectrochemical methods addressing the bandenergetics directly under operational conditions in (mostlyaqueous) solutions. As already mentioned, experimentallythe problem of determination of the band edge positionis typically addressed by the measurement of the flatbandpotential or of the quasi-Fermi level. Several electrochemical,photoelectrochemical, and spectroelectrochemical methodswill be now discussed in more detail.

3. (Photo)electrochemical Methods

3.1. Capacitance Measurements on Thin Compact Films. Asalready noted above, since thin compact TiO2 films (e.g.,dense anodic TiO2 films on Ti) behave similarly to conven-tional macroscopic semiconductor electrodes, the Schottky

formalism can be applied and their conduction band edgepotential can be measured as the flatband potential. Usingthe model of a parallel-plate capacitor, the Mott-Schottkyrelation can be obtained from (2):

1C2

SC= 2

εε0qND

(

Eappl − EFB − kT

q

)

. (11)

The interface double layer capacitances CSC and CH can betreated as two capacitors connected in series (Figure 4(d)).The overall capacitance C is then given by

1C= 1

CSC+

1CH

. (12)

Under some conditions (a single crystal-like behavior, mod-erate doping, surface states neglected), it can be assumed thatthe width of the space-charge layer is much larger than thewidth of the Helmholtz layer, which yields CSC � CH and,accordingly, C ∼= CSC.

A widely used technique for the determination of thecapacitance is the measurement of impedance. In theseexperiments, an ac-voltage signal of small amplitude is usedfor the perturbation of the sample. From the currentresponse, the impedance value and the phase shift can bedetermined. There are essentially two common impedancetechniques, which enable us to get information about thecapacitive behavior of a system. Either the impedancespectrum for a certain range of frequencies is measured(usually under potentiostatic conditions) or one particularfrequency is chosen and the impedance is measured atconstant frequency in dependence on the applied potential.Using the latter technique, the capacitance of the space-charge layer can be calculated from the imaginary part ofmeasured impedance:

Csc = −i2π f Zim

, (13)

where Zim denotes the imaginary part of impedance, i isimaginary unit, and f is the frequency of ac-voltage signal.For determination of Csc, a relatively high frequency isusually chosen and a simple equivalent circuit (neglectingthe capacitive contribution of other elements) is employedfor the interpretation of measured data.

From the resulting Mott-Schottky plot (CSC−2 versus E;

see Figure 6), the flatband potential EFB and the dopingdensity ND can be now obtained as the intercept with thex-axis and from the slope of the linear part. The value of theflatband potential from capacitance measurements on single-crystal anatase is reported to be −0.16 V versus NHE (pH 0)with a Nernstian behavior exhibiting a shift of −0.06 V/pHunit [172]. However, it should be noted that the impedanceresponse of the probed system often contains all contri-butions of the experimental setup, including back contactcapacitance, sample resistance, electrolyte resistance, capaci-tance and resistance of Helmholtz layer and of surface states,which sometimes causes non-ideal behavior and makes itdifficult to obtain reliable values of EFB (see Figure 6) whenusing highly simplified equivalent circuits as in Figure 4(d).

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Advances in Physical Chemistry 9

0

1

2

3

4

5

−0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8

Potential (V versus NHE)

1/C

2(F−2

cm4×1

010) 2 kHz

1 kHz

0.5 kHz

Figure 6: Mott-Schottky plots measured in a LiClO4 (0.1 M; pH 6)electrolyte at three different frequencies on compact anodic TiO2

layers. The frequency dispersion is a frequent phenomenon relatedto the nonideality of the semiconductor.

3.2. Photocurrent Onset Measurements. Another commonmethod for the determination of the position of the conduc-tion band edge is a measurement of the potential dependenceof photocurrent. The principle of photocurrent generationis explained in Figure 7. If a compact n-type semiconductor(like, e.g., a dense anodic TiO2 film on Ti) immersed inthe electrolyte under depletion conditions is irradiated withlight of higher energy than that of its bandgap, electron-hole pairs are generated and separated in the potentialgradient of the space-charge layer (Figure 7(a)). In the caseof an n-type semiconductor, this potential gradient drivesphotogenerated holes toward the semiconductor/electrolyteinterface and electrons toward the interior of the electrodeand from there to the electrical connection to the externalcircuit. Accordingly, anodic (positive) photocurrents aretypically observed at TiO2 photoelectrodes. Obviously, ifwe sweep the potential of the photoelectrode in cathodicdirection (upwards on the potential scale), the band bendingwill be less and less pronounced. The diminished potentialgradient and thickness of the space-charge layer will lead toenhanced recombination of photogenerated charges, whichwill, in turn, lead to constant decrease of photocurrentsduring the cathodic potential sweep. Finally, at the flatbandpotential, the photocurrent should disappear totally [184].Hence, this so-called “photocurrent onset” potential can beconsidered to coincide with the flatband potential and tomerge practically with the conduction band edge.

Interestingly, similar principle applies also in case ofnanocrystalline porous electrodes, in which the photogen-erated charge separation is not controlled by the potentialgradient over the space-charge region since the crystallite sizeis too small to support an effective depletion layer [158, 159].

Here, the photocurrent is determined by the efficiency ofphotogenerated electron/hole transfer at the semiconduc-tor/electrolyte and semiconductor/substrate interface [160–163]. This is schematically illustrated in Figure 7(b) whichshows the mechanism of photocurrent generation at TiO2

particles deposited on the conductive glass substrate (e.g.,ITO). Assuming the presence of suitable redox species inthe electrolyte, photogenerated holes immediately react withthese at the surface of the particles. The photogenerated elec-trons can be transferred to the underlying conductive glasssubstrate, assuming that the Fermi level of the conductiveglass is positive enough. Hence again, by moving the Fermilevel of the ITO electrode cathodically, we should observethe disappearance of photocurrents when the potential ofthe underlying electrode (the Fermi level of ITO) reaches thequasi-Fermi level of TiO2 particles, that is, their conductionband edge. In order to avoid scavenging of photogeneratedelectrons by oxygen dissolved in the solution, the electrolyteshould be deaerated by purging with an inert gas priorto the measurement. Figure 7(c) shows a typical photo-voltammogram recorded under interrupted illumination ona dense compact TiO2 electrode during the cathodic sweep.It should be noted that the absolute values of EC obtainedare sometimes anodically shifted since the recombinationbecomes practically complete already at potentials relativelyfar (0.1–0.3 V) from the conduction band edge. Nevertheless,this method provides valuable information on shifts ofEC, particularly when a direct comparison can be drawnfrom measurements on different samples under otherwiseidentical conditions.

3.3. Open-Circuit Photovoltage Measurements. Apart fromthe capacitance measurements and the photocurrent onsetdetermination, the value of EFB can be also determined fromthe dependence of the electrode open-circuit potential (EOC)on the illumination intensity (Figure 8). Under open-circuitconditions, the photogenerated holes can accumulate atthe surface, which with increasing light intensity lowers thebarrier US (see Figure 3) for electrons until the electrons canreach the surface at the same rate as holes. At the same time,the quasi-Fermi level (measured as EOC) rises because ofthe higher occupancy of the conduction band. Accordingly,at sufficiently high-intensity, EOC becomes constant andthis value is very close to the potential of the conductionband edge [80, 125, 185–187]. In order to avoid reactionof photogenerated electrons with oxygen in the electrolyte,which would decrease the photovoltage, it is necessary topurge the solution with inert gas.

Figures 9(a), 9(b), and 9(c) show EOC versus relative lightintensity plots measured for a compact TiO2 film at differentpH values. It is seen that EOC becomes independent of inten-sity when the latter exceeds relative values of 90%. The EFB

values plotted in Figure 9(d) show a nearly Nernstian lineardependence on pH with EFB = (−0.17±0.02)−0.054(pH) Vversus NHE, in agreement with values reported for anataseTiO2 [172]. Interestingly, the open-circuit photovoltagemethod yields reliable results also in case of nanocrystallinephotoelectrodes [188, 189]. Under high-intensity illumina-tion, the electrons accumulating in the conduction band and

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10 Advances in Physical Chemistry

Red

Electrolyte

E

TiO2

EV

EC

∗EFp

hA

EF =∗EFn

(a)

E

∗EFn

∗EFp RedEF

ITO

(b)

0

5

10

15

20

25

30

−0.6 −0.4 −0.2

Potential (V versus NHE)

0 0.2 0.4 0.6 0.8 1 1.2

Cu

rren

t de

nsi

ty (μ

A/c

m2)

Photocurrent onset”

(c)

Figure 7: Schematic representation of the mechanism of photocurrent generation at a compact (a) and nanocrystalline (b) TiO2 electrode.(c) Photovoltammogram under interrupted illumination for a compact TiO2 electrode (dense anodic layer) recorded in LiClO4 (0.1 M; pH6) electrolyte in the cathodic direction with the sweep rate of 2 mV/s. The incident light wavelength was 350 nm.

Without Irradiation Irradiation

V

Referenceelectrode

Workingelectrode

irradiation Rel. intensity ∼ 50% Rel. intensity ∼ 100%

EOC

EOCEOC

EOC = EFB

Figure 8: Schematic view of the flatband potential determination as the limiting value of the open-circuit potential (EOC) under high relativeirradiation intensity.

traps right bellow the conduction band edge cause the Fermilevel of the conductive glass substrate to shift to the vicinity ofEC of TiO2. It is again emphasized that intense purging withinert gas is absolutely necessary in order to avoid scavengingof photogenerated electrons by oxygen dissolved in solution.

3.4. Spectroelectrochemical Measurements on TransparentFilms. The fact that many nanocrystalline films are trans-parent offers the possibility to determine the position ofthe conduction band edges using the spectroelectrochemicalmethod of Fitzmaurice et al. [190–192]. The principle of

this method is schematically depicted in Figure 10. TheFermi level of ITO, EF (ITO), can be controlled by appliedpotential, whereas the position of the conduction bandedge of the transparent nanocrystalline TiO2, EC (TiO2),depends only on the pH of the solution. At a constant pH,applying potentials more negative than EC (TiO2) leads toinjection of electrons from ITO into the conduction band ofTiO2 (Figure 10(b)). During injection of electrons into theconduction band, the TiO2 nanoparticles are not at thermo-dynamic equilibrium anymore; the Fermi level of TiO2 istherefore properly designated as a quasi-Fermi level, ∗EFn,and practically merges with the conduction band edge, EC.

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Advances in Physical Chemistry 11

0 20 40 60 80 100

Rel. light intensity (%)

−0.25

−0.2

−0.15

EOC

(V v

ersu

s N

HE

)

(a)

0 20 40 60 80 100

Rel. light intensity (%)

−0.55

−0.5

−0.45

EOC

(V v

ersu

s N

HE

)

(b)

0 20 40 60 80 100

Rel. light intensity (%)

−0.85

−0.8

−0.75

EOC

(V v

ersu

s N

HE

)

(c)

−0.2

−0.4

−0.6

−0.8

0 2 4 6 8 10 12 14

pH

EFB

(V v

ersu

s N

HE

)

(d)

Figure 9: Dependence of the open-circuit potential (EOC) on illumination intensity measured in (a) HCl (0.1 M; pH = 1.1), (b) NaCl (0.1 M;pH = 6.9), and (c) NaOH (0.1 M; pH = 12.3). (d) pH dependence of flatband potential (EFB). The electrolyte was degassed by intensebubbling with nitrogen.

CB

VB

E

EC

EFhA1

ITO TiO2

EF(ITO) EC (TiO2)

(a)

E

EF

hA2

ITO TiO2

∗EFn

EF(ITO) EC (TiO2)

(b)

−0.1

0

0.1 780 nm

350 nm

Abs

orba

nce

Potential (V versus NHE)

−0.6−0.8 −0.4 −0.2 0 0.2 0.4 0.6

(c)

Figure 10: Schematic view of the principle of spectroelectrochemical determination of the quasi-Fermi level of nanocrystalline TiO2 (a, b);for details, see the text. (c) Absorbance changes of a transparent TiO2 film at two different wavelengths recorded during a cathodic potentialsweep in a deaerated LiClO4 (0.1 M) solution acidified to pH 2.9.

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12 Advances in Physical Chemistry

Potential (V versus NHE)

−0.6−0.8−1−1.2 −0.4 −0.2 0 0.2 0.4 0.6

pH 11.5 pH 2.9

Abs

orba

nce

at

780

nm

0

0.02

0.04

(a)

3 4 5 6 7 8 9 10 11 12

pH

−0.3

−0.4

−0.5

−0.6

−0.7

−0.8

−0.9Qu

asi-

Ferm

i lev

el (

V v

ersu

s N

HE

)

∗EFn = (−0.21± 0.05)−0.058 (pH) V versus NHE

(b)

Figure 11: (a) Absorbance changes (at 780 nm) of a transparentnanocrystalline TiO2 film recorded during a cathodic potentialsweep in a deaerated LiClO4 (0.1 M) solution with adjusted pH.The arrows indicate potentials at which the values of quasi-Fermilevel were read off. (b) pH dependence of quasi-Fermi levels ofa transparent nanocrystalline TiO2 film. Measurements were per-formed outside the neutral pH range in order to avoid pHfluctuations due to reduction of protons [206].

The occupation of states near the conduction band edgeresults in a shift to higher energies of the bandgap absorptionedge (i.e., hν2 > hν1 in Figures 10(a) and 10(b))—the so-called Burstein-Moss shift [193, 194]. From the spectroscopicpoint of view, this has two consequences. First, at potentialsmore negative than EC (TiO2), the difference in absorbanceat wavelengths lower than the typical absorption band edge(e.g., at 350 nm) becomes negative. Second, the absorbanceat 780 nm increases due to the intraband transitions of freeelectrons in the conduction band (Figure 10(c)) [190, 191,195].

In this context, it should be noted that the nanocrys-talline TiO2 has often a high density of electron traps thatare distributed exponentially in the bandgap below the con-duction band edge [196–200]. These traps can be obviouslyfilled at potentials slightly more positive than EC and canalso contribute to absorbance changes. This means that inpractice it might be difficult to discern where exactly the risein absorbance coincides with the potential of the conductionband edge. Figure 11(a) shows the absorbance changes atλ = 780 nm of a transparent nanocrystalline TiO2 film at twodifferent pH values. The potentials of ∗EFn were in this case,somewhat arbitrarily, read off at points where the absorbancechange was approximately 0.005. The ∗EFn values (which

coincide with the EC values) plotted in Figure 11(b) showa nearly Nernstian linear dependence on pH with ∗EFn =(−0.21± 0.05)− 0.058(pH) V versus NHE.

3.5. Quasi-Fermi Level Measurements on TiO2 Powder Sus-pensions. In the field of heterogeneous photocatalysis, TiO2-based materials are often employed in the form of nanocrys-talline powders. The quasi-Fermi level of electrons, ∗EFn, canbe in case of powder suspensions determined by the methodof Roy et al. [29, 201] that draws on a similar method intro-duced previously by Bard et al. [202–204] In Roy’s method,the pH dependence of the potential of a platinum electrodeimmersed in an irradiated suspension of a semiconductorpowder (Figure 12) is recorded in the presence of an electronacceptor with pH-independent reduction potential. As anelectron acceptor, MV2+ (methyl viologen; 1,1′-dimethyl-4,4′-bipyridinium dichloride; EMV2+/+• = −0.45 V versusNHE) [130] is typically used (Figure 12(b)).

The principle of the method is depicted in Figure 13. Atthe beginning of the measurement, the pH of the solutionis very low and the electrons generated in the conductionband do not have enough reducing power to reduce MV2+

(Figure 13(a)). Upon increasing the pH of the solution, theband edges of TiO2 shift to more negative potentials (seeabove Section 2.2), which makes at some point the electrontransfer to MV2+ in the electrolyte possible (Figure 13(b)).The platinum electrode serves as a simple redox electrodein this case, and its potential shifts more negative withthe increasing concentration of the reduced form of methylviologen (MV+•) in the solution. The inflection point (pH0)of the potential-pH curve (Figure 12(c)) determines thepH value at which ∗EFn coincides with EMV2+/+• . AssumingNernstian shift of band edges (0.059 V/pH unit) [125],

∗EFn = EMV2+/+• + 0.059(

pH0 − pH)

. (14)

Using this procedure, ∗EFn at pH = 7 of anatase TiO2 powder(Hombikat UV 100) was determined as−0.60±0.02 V versusNHE, which is in a very good agreement with reportedvalues for single-crystal anatase (−0.58 V versus NHE) [172].It should be also noted that efficient scavenging of photo-generated holes is essential during these measurements. Insome cases—on doped or surface-modified TiO2 samples,for example—an additional hole scavenger must be added inorder to avoid severe recombination. Such a scavenger shouldbe very easily oxidizable (e.g., iodide), and at the same timeit should not produce strongly reducing radicals upon one-hole oxidation (e.g., ethanol, isopropanol) since these arealso able to reduce MV2+, which would falsify the resultingvalues of ∗EFn [205].

4. Conclusions

TiO2 nanomaterials play a key role in the development ofvarious kinds of photochemical systems and devices, par-ticularly in the field of heterogeneous photocatalysis andphotoelectrochemistry. In the last years, we have witnessed areal boom of diverse strategies for fabrication of new types ofTiO2-based materials showing an extreme variety in terms of

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Advances in Physical Chemistry 13

V

Pt electrode

Ag/AgClref. electrode

pH electrode

IR waterfilter

150 WXenon arc lamp

N2

(a)

H3C+N N+ CH3

(b)

pH

6 74 52 3

−0.6

−0.4

−0.2

0

0.2

Pote

nti

al (

V v

ersu

s A

g/A

gCl)

pH0

(c)

Figure 12: (a) Schematic view of the experimental setup for the determination of quasi-Fermi level for electrons using the method of Roy. A60 mL solution of KNO3 (0.1 M) with a small amount of MV2+ is bubbled through with nitrogen in order to avoid the reoxidation of MV+•

by dissolved oxygen. (b) Structure of MV2+. (c) Determination of the value of pH0 from a typical potential versus pH curve.

E

hA

∗EFn

pH < pH0

CB

VB

x

MV2 + /MV+•

(a)

E

hA

∗EFn CB

VB

MV2 + /MV+•

pH pH0

(b)

Figure 13: Schematic view of the principle of the determination of ∗EFn. Upon increasing the pH of the solution, the band edges of asemiconductor shift to more negative potentials. At pH = pH0, the value of ∗EFn matches the reduction potential of a pH-independent redoxspecies in the electrolyte (MV2+).

composition, morphology, and surface properties. Althoughthe knowledge of the position of the band edges on thepotential scale is a crucial prerequisite for understanding thephotoactivity of the system and for further optimization ofits performance, it has been in recent years typically only

rarely directly experimentally addressed. In this paper it hasbeen shown that in case of TiO2 the general strategy for bandedges determination usually consists in the measurementof the flatband potential and/or the quasi-Fermi level ofelectrons. Apart from “classical” approaches (capacitance

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14 Advances in Physical Chemistry

measurements) developed in the field of semiconductorphysics for well-defined samples in the form of single crys-tals, several novel techniques have been developed recently.These are particularly important since they are also suitablefor measurements on non-ideal nanostructured, porous,and particulate materials, which represent the majority ofcurrently newly developed materials. The methods dis-cussed above included elaborate photoelectrochemical andspectroelectrochemical methods applicable on compact andnanocrystalline thin films, as well as on powder suspensions.Obviously, in case of many systems, a combination of severalmethods will give a more solid and complete assessment ofthe energetics at the solid/solution interface. It is hoped thatthis paper will serve as a useful resource for many scientistsworking in the field of photoactive nanomaterials and asan impetus for the development of further methods thatwill allow for better understanding and improvement of thephotoactivity of photochemical systems and devices.

Acknowledgments

The financial support by the MIWFT-NRW within theproject “Anorganische Nanomaterialien fur Anwendungenin der Photokatalyse: Wasseraufbereitung und Wasserstoff-gewinnung” and the support by the Center for Electro-chemical Sciences (CES) are gratefully acknowledged. Thecompany Sachtleben Chemie is acknowledged for providinga free sample of Hombikat UV 100.

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